Curve name  $X_{227}$  
Index  $48$  
Level  $16$  
Genus  $0$  
Does the subgroup contain $I$?  Yes  
Generating matrices  $ \left[ \begin{matrix} 3 & 3 \\ 0 & 3 \end{matrix}\right], \left[ \begin{matrix} 7 & 0 \\ 0 & 7 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 1 \end{matrix}\right], \left[ \begin{matrix} 5 & 0 \\ 0 & 3 \end{matrix}\right]$  
Images in lower levels 


Meaning/Special name  
Chosen covering  $X_{84}$  
Curves that $X_{227}$ minimally covers  $X_{84}$, $X_{118}$, $X_{120}$  
Curves that minimally cover $X_{227}$  $X_{477}$, $X_{479}$, $X_{488}$, $X_{494}$, $X_{227a}$, $X_{227b}$, $X_{227c}$, $X_{227d}$, $X_{227e}$, $X_{227f}$, $X_{227g}$, $X_{227h}$, $X_{227i}$, $X_{227j}$, $X_{227k}$, $X_{227l}$  
Curves that minimally cover $X_{227}$ and have infinitely many rational points.  $X_{227a}$, $X_{227b}$, $X_{227c}$, $X_{227d}$, $X_{227e}$, $X_{227f}$, $X_{227g}$, $X_{227h}$, $X_{227i}$, $X_{227j}$, $X_{227k}$, $X_{227l}$  
Model  \[\mathbb{P}^{1}, \mathbb{Q}(X_{227}) = \mathbb{Q}(f_{227}), f_{84} = \frac{f_{227}}{f_{227}^{2}  \frac{1}{4}}\]  
Info about rational points  None  
Comments on finding rational points  None  
Elliptic curve whose $2$adic image is the subgroup  $y^2 + xy = x^3  x^2 + 58950x + 26038750$, with conductor $1530$  
Generic density of odd order reductions  $25/224$ 